Proceedings of SALT 26: 664–683, 2016 A demonstration-based account of (pluractional) ideophones * Robert Henderson University of Arizona Abstract This paper develops a novel formal semantics of ideophones that can account for their meaning and compositional properties. The proposal extends recent work on iconicity in sign languages in Davidson 2015, whose demonstration- based framework provides a formal foundation for the semantics of ideophones that captures the difference between descriptive meaning and depictive meaning, the kind of meaning ideophones traffic in. After providing a demonstration-based account of the basic ideophone construction in the Mayan language Tseltal, the paper then shows how the demonstration-based account can be used to analyze pluractionality in the ideophone domain. In particular, through case studies on Tseltal and Upper Necaxa Totonanc (Totonacan), I show that there are two previously unrecognized types of ideophonic pluractionality, and that their properties support the demonstration-based account. Keywords: ideophones, pluractionality, iconicity, demonstrations, Mayan, Totonacan 1 Introduction The term ideophone is used to pick out a distinguished class of words in a language that specialize in depicting sensory imagery (Dingemanse 2011: p. 25; 2012). While the expressions considered in this work fit the definition, ideophones are often easier to point at than define. For this reason, consider the following example of the ideophone tsok’ in Tseltal (Mayan). (1) pura ch’il-bil-Ø, tsok’ x-chi-Ø ta mantekat just fried-PERF-B3 IDF:sound.start.to.fry NT-say-B3 P lard ‘it just gets fried, it goes «tsok’» in the lard’(Pérez González 2012: p. 162) The literature on the formal semantics of ideophones is scarce. This is, I think, * I would like to thank Scott AnderBois, Diana Archangeli, Rebekah Baglini, Dylan Bumford, Simon Charlow, Lucas Champollion, Kathryn Davidson, Jeremy Kuhn, Heidi Harley, and Jaime Pérez González for extremely helpful discussions about ideophones and iconicity. I need to thank David Beck and Susan Smythe Kung for talking with me about Totonacan languages and Elena Mihas for clarifying some points in Alto Perené. I also need to thank a group of UA faculty and students for comments on this presentation. ©2016 Henderson Demonstrations and ideophones due to two challenges: (i) it is not at all clear how to formalize the distinction between descriptive meaning, which is at the heart of truth-conditional semantics, and depictive meaning, which ideophones seem to traffic in, and (ii) the idiosyncractic specificity of ideophone meaning and their restricted (morpho)syntactic distribution presents obstacles for doing formal lexical semantics. In particular, by avoiding modification and appearing as arguments to only a small class of verbs, it is difficult to isolate their meaning and to determine their type. The goal of this paper is to address both of these problems, and in doing so, begin to develop a formal semantics of ideophones that can account for their meaning and compositional properties. To address the first problem, I propose an analysis of ideophones that extends recent work in Davidson 2015, which provides a novel unified account of quotation and a variety of iconic phenomena in sign language in terms of a demonstrations—a special type of communicative event that stands in a similarity relation with the event demonstrated. The demonstration-based framework will provide a formal foundation for the semantics of ideophones that can capture the difference between description and depiction. Addressing the second problem is more complex because it means exploring the range of ideophone meaning and making comparisons to the meanings of expressions from more well-known categories. While pluractional meaning is often idiosyncratic, many ideophones clearly have pluractional semantics (i.e., they make reference to plural events). Since the typology of pluractional meaning is fairly well understood (Hofherr & Laca 2012; Wood 2007, among many others), it provides exactly the hook into problem that we need. We can group ideophones by the variety of pluractionality they exhibit, and then provide templates that generalize over particular items to capture this aspect of ideophone meaning. Along these lines, this paper shows through case studies on two Mesoameri- can languages, Tseltal (Mayan) and Upper Necaxa Totonac (Totonacan), that there are two broad types of ideophonic pluractionality and that their form supports the demonstration-based analysis. The first, which I call “demonstration-external plurac- tionality”, involves a speaker using an ideophone to do a plurality of demonstrations that characterize a plurality of events. The second kind of ideophonic pluractionality, which I call a “demonstration-internal pluractionality”, is much more similar to pluractionality in the verbal domain. It involves morphology that derives ideophones that can only be used to demonstrate plural events. 2 Demonstration-based theory of quotation When thinking about quotation, we usually think about verbatim quotation, where the act of quotation concerns the words used. For instance, suppose Mary says (2). (2) I play guitar. 665 Henderson Mary can then be quoted as in (3), where words alone ensure the quotation is true. (3) Mary was like “I play guitar”. While this is maybe the most salient situation, it is well known that be like-quotation can be felicitously used to replicate a variety of aspects of an event (Clark & Gerrig 1990; Davidson 2015, among others). For instance, words can be used to “quote” an agent’s behavior or inner monologue, even if those particular words are not used, as shown in (4) where the the quotative sentence is judged true even though the cat never uttered the quoted words. (4) My cat meows loudly and paces around its food bowl. a. My cat was like “feed me!” (Davidson 2015: ex. 21) Davidson’s 2015 proposal, following earlier work by Clark & Gerrig(1990), is to say that verbatim quotation is merely a special case of what we see in (4). The theory that unites them says that all quotation involves the performance or demonstration of an event. One can demonstrate or perform an event by performing the words that occur in it—i.e., verbatim quotation—but one can also perform all sorts of aspects of the event, including intonations, facial expressions, thoughts, etc. The downside to this kind of theory is that, as we will see, we have to radically underspecify the truth conditions for quotative sentences. But, this might just be a bullet we have to bite. The core idea in Davidson 2015 is that there is a distinguished subset of events, namely a class of events with communicative intent she calls demonstrations.1 Davidson(2015) gives demonstrations their own type d, and while not formalized, the intended interpretation is that d is a subtype of e—the type of events.2 To implement this, the backdrop for the account is lax many-sorted type logic. Lax just means that (i) we do not require domains for sorts to be disjoint, and (ii) equality (and only equality) is type agnostic—e.g., s = s 0 is a formula even if s and s 0 are terms with different types. Below are the highlights of the setup that are necessary for understanding the analysis. The domain of individuals of type e is the powerset of a designated set of entities + IN minus the empty set: De = Ã (IN) = Ã(IN) n /0. In addition to the domain of individuals, I additionally assume, following Hinrichs 1985; Bach 1986; Link 1998, 1 Note that while this section is heavily based on Davidson’s work, I have altered some things and made assumptions about the domains of events, demonstrations, and linguistic expressions that she might not agree with. When it’s clear that I have diverged from her work, I note it in the text. 2 This could be implemented in some variety of lambda calculus with subtyping, like F< (see Retoré 2014) or TCL (see Asher 2011). I do not take this route because I do not need all the power these systems provide, and the resulting models become fairly complicated. I will instead work with a more familiar many-sorted type logic. The trade off, of course, is that I will need additional quantifiers, relations, etc. over new types, but I believe that the result is manageable. 666 Demonstrations and ideophones structured domains of events and times. The domain of events of type e is the + powerset of a designated set of events EV minus the empty set: De = Ã (EV) = Ã(EV) n /0. The domain of times of type t is the powerset of a designated set of times TM minus the empty set, and is additionally partially ordered by ≺ (temporal + precedence): Dt =Ã (TM) =Ã(TM) n /0. Finally, following Davidson 2015, we add the novel domain of demonstrations of type d, which is powerset of a designated + set DM ⊂ EV minus the empty set: Dd = Ã (DM) = Ã(DM) n /0. Note that the domain of demonstrations is a subset of the domain of events. I want to think of demonstrations as events of communication under a particular guise that allows certain constructions, like be like-quotatives or ideophone constructions, to extract their communicative intent. Atomic individuals and atomic events are the singleton sets in Ã+(IN), Ã+(EV), Ã+(DM) respectively; they are identified by a predicate ATOM (which I’ll apply to individuals, events, and demonstrations disambiguated by context). The “part of” relation ≤ over individuals / events / times / demonstrations (disambiguated context) is set inclusion over Ã+(IN) / Ã+(EV) / Ã+(TM) / Ã+(DM): a ≤ b iff a ⊆ b. Finally, sum operation ⊕ (disambiguated by context) is set union overÃ+(IN) / Ã+(EV) / Ã+(TM) / Ã+(DM): a ⊕ b := a [ b. As is common, events are connected to the domains of individuals and times via q-role and trace functions.